PSG, the reigning Ligue 1 champions, were among those heavily linked with Manchester United striker Rooney over the summer - amid talk that he was pushing for an Old Trafford exit.
United made it clear that they would not be sanctioning a sale and the England international saw out the window on their books.
Silva, though, believes there may be further opportunities to put a deal in place - with it possible that PSG will renew their interest in January or again in 2014.
He told the Sunday Mirror: "I was hopeful we would sign Wayne Rooney this summer and I am hopeful that we still can.
"It is clear his future at Manchester United is not certain.
"The player himself has made it clear that he would like a new challenge.
"If he still feels that way in January or even next summer then, once again, I would urge him to come and join PSG.
"We are the most exciting project in European football and it is clear from the ambition of our owners that we are going to be successful."